Martin J. Walsh’s smile was brighter and there was a little more pep in his step Monday as he swept through Mission Hill on the eve of the first public judgment of his job so far as mayor.

“I feel good about [Tuesday’s preliminary election],’’ Walsh said, noting his campaign’s get-out-the-vote push last weekend that included volunteers “knocking on tens of thousands of doors,” making 50,000 phone calls, and racking up political endorsements, including from Attorney General Maura Healey.

His main challenger, City Councilor Tito Jackson, was also in a mad push for votes. He spent Monday in a whirl of campaign stops, radio interviews, and visits to senior centers, where he implored some of the city’s most loyal voters to show up and check his name on the ballot.

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“I’m excited, I’m energized, and I’m optimistic,’’ said Jackson.

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After months of campaigning and arguing past each other, Walsh and Jackson will square off in a run-off contest that also includes two lesser-known candidates, Robert Cappucci, a retired police officer, and Joseph Wiley, a customer service representative for MassHealth. Polls are open Tuesday from 7 a.m. to 8 p.m.

The two candidates with the most votes will run in the municipal election on Nov. 7.

The preliminary contest will be a test for Jackson and Walsh, both sons of Dorchester. For Walsh, a former labor leader, the vote will mark an initial review of his leadership. For Jackson, the adopted son of Grove Hall activists, it will be a test of the city’s appetite for political change.

Only 15 percent of the registered voters are expected to turn up Tuesday, according to Secretary of State William F. Galvin. And some residents interviewed Monday — from South Boston to East Boston — expressed little interest in the race.

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“It doesn’t feel like there is any election at all,” said Migdalia Reyes, who works two jobs, as a housekeeper and at Dunkin’ Donuts, as she waited for a bus at Maverick Square in East Boston, one of the few neighborhoods to have a competitive race for city councilor. To prove her point, she turned in a circle to point out that there was no one holding political signs nearby.

“You don’t see it,” she said. “I don’t feel it either.”

Matthew J. Lee/Globe staff

Tito Jackson campaigned on the corner of Malcolm X Blvd and Tremont Street on Monday.

Mike Luizzo, 33, a software analyst from South Boston, which also has a competitive City Council race, said he too has little interest, though he follows national politics.

‘I’m just not even paying attention to it,” he said. ‘It’s been kind of flat.”

Voters who are tuning in to the mayoral race said there isn’t much to keep them excited.

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“Who’s running?’’ asked Jim Harris in jest on Monday morning, as he opened the liquor store he co-owns near Forest Hills. “Tito and the other guy that’s in office.”

The Hyde Park resident said he wasn’t voting for either. Harris criticized Jackson for supporting a massive pay raise for councilors and said Walsh’s policies put the squeeze on small businesses like his.

But Denise Upshaw, a 59-year-old Fields Corner resident, said she is ready to give the mayor another chance.

“He has a lot to say,’’ she said of Walsh. “But he hasn’t been in office long enough to make an impact in the city’’ as of yet.

Brian Walsh, a retired West Roxbury resident, is leaning toward Jackson, he said, noting the councilor’s support for legalizing recreational marijuana as a way to boost the local economy.

“I get the impression from [Jackson] that he knows the city,’’ he said. “I feel like he is closer to the city than the mayor is.”

But Ricardo Anderson,a 54-year-old retired Boston firefighter, said he is not too sure about the councilor, whom he said he respects and admires.

“I love Tito, but I don’t think the people of Boston are dissatisfied right now,’’ said Anderson, who did not say who he would vote for. Anderson likes Jackson, but he has doubts.

“I don’t think Boston is ready for a black mayor,’’ he said.

Anderson also said Walsh should do a better job advocating for more minorities in the local unions and the fire department.

Across the city, people are still waking up to the idea of an election, but the campaigns were working to get noticed. A Walsh volunteer erected a campaign sign in a restaurant in Dudley Square, while a man was driving a sedan that carried loudspeakers blasting out the news that the vote was Tuesday. “Vote Tito Jackson,’’ he said.

Walsh spent the morning on a walk through Mission Hill, shaking hands and taking pictures with business owners and residents.

“The response feels really good, really positive,’’ Walsh said. “It should be a warm day [Tuesday], and that should drive up the turnout numbers a little bit.”

He stopped in AK’s Takeout & Delivery, where the owner served Walsh and his aides slices of pizza. He then stopped by nearby Butterfly Coffee, posing with the owners before heading to Egleston Square.